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Naked Triplets

Although Naked Triplets are fairly hard to see, it is still one of the moderately difficult methods.

A Naked Triplet occurs when the cumulative list of candidates in three fields of a logical unit comprises exactly three candidates. In this case, these candidates can be deleted from all fields of the logical unit which do not belong to the Triplet.

It is difficult to see because a single Naked Triplet may have a number of forms.
Look at the following lines. They contain some possible manifestations of a Naked Triplet with the candidates 2, 4 and 7. Each line contains possible candidates for the fields of the triplet:

  • 247 - 247 - 247
  • 247 - 24 - 247
  • 47 - 24 - 247
  • 27 - 47 - 24

These are all the same Triplet. Each field must contain at least two of the candidates in the group and must not contain any candidate that is not in the group.
In such a constellation, it is obvious that, in the end, each of the three fields in the group must get one of the three candidates in the group. Consequently, the three candidates cannot be valid in any other field in the logical unit.

Can you guess what to expect from the Quadtuplets and Quintuplets to you? Exactly! They have more variants ...

The green fields represent a Naked Triplet made up of the candidate group 4,6,9.

As a consequence, the 6 or the 9 can be deleted from the yellow fields.

Sudoku example naked Triplet

Once that's done, it produces the next Naked Triplet, made up of the candidate group 1,5,7.

This time, the candidates 1 and 7 can be deleted from the yellow field.

Hurrah! This leads to a completed field, a rather rare occurence in the higher methods.
This distinguishes the higher methods from the basic methods, which always result in completed fields when they work.

The Naked Triplet is the first "normal" member of the family of Naked groups.

Sudoku example naked Triplet

see also: Generalization: Naked groups

 

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